Abstract
We study variants of the potato peeling problem on meshed (triangulated) polygons. Given a polygon with holes, and a triangular mesh that covers its interior (possibly using additional vertices), we want to find a largest-area connected set of triangles of the mesh that is convex, or has some other shape-related property. In particular, we consider (i) convexity, (ii) monotonicity, (iii) bounded backturn, and (iv) bounded total turning angle. The first three problems are solved in polynomial time, whereas the fourth problem is shown to be NP-hard.
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Work by B.A. has been supported in part by a grant from the U.S.-Israeli Binational Science Foundation and by NSA MSP Grant H98230-06-1-0016. Partially funded by the Netherlands Organization for Scientific Research (NWO) under FOCUS/BRICKS grant number 642.065.503, and under the project GOGO.
A preliminary version of this paper was presented at the 19th Canadian Conference on Computational Geometry (CCCG 2007), under the title “Largest Subsets of Triangles in a Triangulation”.
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Aronov, B., van Kreveld, M., Löffler, M. et al. Peeling Meshed Potatoes. Algorithmica 60, 349–367 (2011). https://doi.org/10.1007/s00453-009-9346-8
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DOI: https://doi.org/10.1007/s00453-009-9346-8